Question
Expand using suitable identity: $(x+2 y+4 z)^2$
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Answer
$(x+2 y+4 z)^2$
$=(x)^2+(2 y)^2+(4 z)^2+2(x)(2 y)+2(2 y)(4 z)+2(4 z)(x)$
(Using Identity $(a+b+c)^2=a^2+b^2+c^2+2 a b+2 b c+2 c a$ )
$=x^2+4 y^2+16 z^2+4 x y+16 y z+8 z x$
$=(x)^2+(2 y)^2+(4 z)^2+2(x)(2 y)+2(2 y)(4 z)+2(4 z)(x)$
(Using Identity $(a+b+c)^2=a^2+b^2+c^2+2 a b+2 b c+2 c a$ )
$=x^2+4 y^2+16 z^2+4 x y+16 y z+8 z x$
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